Question

Magnetic field at the center of regular hexagon of side ${}^{\prime }{a}^{\prime }$ carrying current ${}^{\prime }{i}^{\prime }$ is

• A. $\frac{{\mu }_0}{\pi }\frac{i}{a}$
• B. $\frac{{\mu }_0}{2\pi }\frac{i}{a}$
• C. $\frac{4}{\sqrt{3}}\frac{{\mu }_{0}i}{\pi a}$
• D. $\sqrt{3}\frac{{\mu }_{0}i}{\pi a}$

Answer 1

The correct option is D $\sqrt{3}\frac{{\mu }_{0}i}{\pi a}$

$\theta ={30}^{\circ }$
OC = $\frac{\sqrt{3}}{2}$ a
Field due to AB at O is,
$B_1=\frac{{\mu }_0}{4\pi }\frac{i}{oc}(\sin \theta +\sin \theta )$.
$B_{net}=6\times B_1=\sqrt{3}\frac{\mu o}{\pi }\frac{i}{a}$